re-thinking uncertainty

Re-thinking uncertanty: A choice-based approach

The overarching aim of this research project is to improve our understanding of uncertainty, its quantification and its communication. It sets out to do so by addressing a set of key epistemological questions that arise in the construction of formal models of rational decision- making. Its expected results will throw new light one of the most fundamental problems in the multidisciplinary field of uncertain reasoning: How to identify an efficient trade-off between foundational robustness and expressive power in the quantification of uncertainty.BackgroundOur need to quantify uncertainty arises primarily in relation to choice problems, i.e. when we must select one from a set of alternatives each yielding a (partially) unknown outcome. Yet, some choice problems lead to an easier quantification of the related uncertainty than others. Suppose a normal-looking die is about to be rolled. In the absence of other relevant information it is entirely plausible to believe that a particular side, say “3”, will show with probability 1/6. The underlying reasoning goes along the following lines: The problem at hand clearly admits of six mutually exclusive outcomes, one of which will certainly occur, and none of which appears to be more likely than the others – hence it would seem irrational of us to give a particular side a probability other than 1/6. Compare this with a situation in which we must decide whether to buy stocks of a certain bank who has invested heavily in Greek bonds. We are told that in the event of Greece exiting the Eurozone, Greek bonds will be completely worthless. Yet the stocks offer very good prospects of profit in a six-month time horizon. In order to make a rational decision we must estimate the likelihood (i.e. choose a representation for our uncertainty) that Greece will exit the Eurozone within the next six months – an event which is often referred to as “GREXIT” in the financial sector. The reasoning we confidently used to choose our probability for the event “3 by rolling a normal-looking die” certainly doesn’t seem to be applicable to GREXIT. In particular there seems no unique way of telling a priori what set should be partitioned in order to define a standard probability distribution.

This project is funded by the European Commission under the Marie Curie IEF-GA-2012-327630 project Rethinking Uncertainty, and it is part of the LSE's Managing Severe Uncertainty project.

output

articles

Giaquinta, M., & Hosni, H. (2015). "Mathematics in the social sciences: reflections on the theory of social choice and welfare". Lettera Matematica. doi:10.1007/s40329-015-0093-1

“Stability for non-standard imprecise probabilities” (with F. Montagna) in 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, July 2014, Montpellier.

Possibilistic expectation in the selection of multiple Nash equilibria (with E. Marchioni), 11th Conference on Logic and the Foundations of Game and Decision Theory July 27-30, 2014, University of Bergen